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名詞

eigenvector (plural eigenvectors)

1. (linear algebra) A vector that is only scaled (not rotated out of its span) under a particular linear transformation; a left or right eigenvector depending on context; (more formally) given a linear transformation A, a vector x such that Ax=λx [or xA=λx] for some scalar λ (called the eigenvalue).

   Synonyms: characteristic vector, latent vector, proper vector

   • (Can we date this quote?), “Lesson 11”, in University College London‎, 8.2 Method to find eigenvalues and eigenvectors, page 1:

     Both equations give the relation x₁ = −x₂. Therefore the set of eigenvectors corresponding to λ = 2 is given by: […] An eigenvector corresponding to λ₁ = 2 is ( −1 1 ).

2. (physics, engineering) A right eigenvector; given a matrix A, the eigenvector of the transformation "left-side multiplication by A."

使用する際の注意点

• Eigenvector has become the standard term in English, but proper vector was formerly more common.
• The concepts of 'eigenvector and eigenvalue arose from the study of quadratic forms and differential equations. Nowadays, they are normally introduced in the context of linear algebra.
• A linear transformation can always be represented as a matrix if the vector space is finite-dimensional (usually a safe assumption in physics).
• In consequence of the rules of matrix multiplication, left eigenvectors are row vectors, while right eigenvectors are column vectors. The convention of right eigenvector as "standard" is fundamentally an arbitrary choice.

派生語

関連する語

Further reading

• eigenvector on Wikipedia.Wikipedia

参考

• Mathworld article on eigenvectors